150 T H E MECHANICS OF THE EARTH'S ATMOSPHERE. 



one could make use of the liquids employed by Plateau, namely, oil and 

 alcohol of equal specific gravity. The question will here arise, in what 

 manner the formation of a jet is modified by capillary action. 



(c) A stream of air in moving air, the latter being made visible by 

 smoke. 



viii. 



The results of the present investigation can be summarized in the 

 following theorems : 



(a) The viscosity of fluids does not prevent the formation of steady 

 discontinuous fluid motions. In consequence of friction these motions 

 in the beginning suffer important modifications by reason of simultane- 

 ous spiral movements; but with long continued flow they form sharply 

 defined fluid jets. 



(b) The jets thus formed are very stable for small velocities, and even 

 after small perturbations again immediately assume their origiual form. 

 For greater velocities, on the other hand, they become very sensitive. 

 If the velocity exceeds a certain limiting value, then only very short 

 jets form in the immediate neighborhood of the opening. 



(c) The jets are not only modified in their movement by solid bodies 

 but also by the liquid adhering to these. The latter adherent liquid is 

 slowly pushed aside by the jet. If then the body is bounded by a con- 

 tinuously curved surface the flowing liquid surrounds it in a thin layer. 

 If, on the other hand, the solid body is bounded by a surface that at 

 certain points has an indefinitely large curvature, such as a sharp edge, 

 then the stream lines follow it only up to this edge and from that point 

 on leave the solid body. 



(d) The theory of discontinuous fluid motions, as Helmholtz and Kirch- 

 hoff have thus far developed it [for perfect fluids], also gives in general 

 the phenomena observed in a fluid subject to friction. The only differ- 

 ence is the formation of vortex motions simultaneous with origination 

 of the jets. 



In conclusion we may call attention to the fact that in nature we find 

 a whole series of processes that have a common origin with those just 

 described. These are to be observed in the currents in rivers and canals, 

 especially at places where the banks have sharp corners or where solid 

 bodies, like the piers of a bridge, retard the uniform movement. The 

 eddying motions there occurring clearly show where the quiet and the 

 moving liquids border on each other. Since as a specially noteworthy 

 result of the investigation here communicated has been to show that 

 discontinuous motions arise even for very small differences of pressure, 

 therefore it is easy to see that they must occur often enough in the last 

 mentioned streams. 



